I calculated a numerical solution (by Runge Kutta) of an oszillation with a final time t and n steps in between.

Now if i plot the solution in position space it works fine, if n>>t. But in this case the DFT looks really strange (see attachement).

If n~t, the frequency space looks good or at least I can see a lorenzian shape somewhere not near bin 0 or bin n, but the resolution is too bad in the position space. Why does the DFT behave this way? Is it already a uncertainty principle or can I fix it somehow?